Details

sample109.0ms

Algorithm

intervals

Results

24.0ms	25×	body	2560	valid
22.0ms	45×	body	1280	valid
20.0ms	184×	body	80	valid
7.0ms	17×	body	640	valid
7.0ms	69×	body	80	nan
2.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify124.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

132.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
120.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
61.0ms	(- (* b b) (* 4.0 (* a c)))
116.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts

118 → 118

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	193	2476
1	481	2169
2	1421	1861
done	5001	1789

prune457.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
22.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
23×	`add-exp-log`
22×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`add-cbrt-cube`
10×	`prod-exp`
8×	`add-log-exp`
7×	`pow1` `fma-neg` `associate-r`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`times-frac`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

247.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
92.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
26.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
114.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
84.0ms	(- (* b b) (* 4.0 (* a c)))
111.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

127 → 127

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	219	2739
1	538	2324
2	1661	1964
done	5000	1892

prune517.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* a c) 4.0))) b) (* 2.0 a))
0.4b	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
1.2b	(- (* b b) (* (* a c) 4.0))
22.9b	(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

118.0ms	(/ (- (sqrt (- (* b b) (* (* a c) 4.0))) b) (* 2.0 a))
72.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
19.0ms	(- (* b b) (* (* a c) 4.0))
24.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (- (sqrt (- (* b b) (* (* a c) 4.0))) b) (* 2.0 a))
154.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
68.0ms	(- (* b b) (* (* a c) 4.0))
93.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	193	2476
1	479	2169
2	1418	1861
done	5000	1789

prune406.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* a c) 4.0))) b)))
0.4b	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
1.2b	(- (* b b) (* (* a c) 4.0))
22.9b	(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

84.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* a c) 4.0))) b)))
98.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
18.0ms	(- (* b b) (* (* a c) 4.0))
24.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* a c) 4.0))) b)))
116.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
82.0ms	(- (* b b) (* (* a c) 4.0))
123.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

simplify1.5s

Counts

164 → 164

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	259	4025
1	584	3484
2	1627	3082
done	5000	2938

prune484.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes204.0ms

Accuracy

84.3% (4.5b remaining)

Error of 10.0b against oracle of 5.5b and baseline of 34.1b

bsearch225.0ms

Steps

Iters	Range		Point
7	1.5383510854529177e-107	7.914847206339754e-106	4.718890261991469e-106
10	-2.386196042261592e+160	-1.0923850232644114e+143	-1.119811545308531e+143

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	31	38
done	31	38

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	5848×	body	80	valid
604.0ms	1056×	body	2560	valid
538.0ms	922×	body	1280	valid
360.0ms	2941×	body	80	nan
180.0ms	479×	body	640	valid
63.0ms	113×	body	5120	valid
49.0ms	208×	body	320	valid
16.0ms	109×	body	160	valid